Download AC Waves. Because waves are the basis of so many signals in

AC Waves.
Because waves are the basis of so many signals in electronic circuits, it is important that
engineers and technicians can make measurements of the important characteristics of
the waves used in AC technology. When AC is mentioned, perhaps the first thing that
comes to mind is the "mains" or "line" supply that brings electricity to homes, factories
and offices. There are many different applications of AC, and although the meaning of
AC, is "Alternating Current" (a current that alternates its direction of flow around a circuit)
"AC" is often used in other terms such as "AC signal" and even "AC voltage". Whenever
the current in a circuit alternates, so will the voltage, and an alternating voltage will of
course, cause an alternating current, even though in many cases one or other of these
properties (voltage or current) may be so small as to be insignificant.
Complex Signal Waveforms
These alternating currents and voltages come in very many forms, the electricity power
supply of course, and all sorts of other signals too. Sound, light, video, radio, all produce
signals that alternate; meaning, they change their values over time, alternating above
and below a particular value (often, but not always zero). Our bodies also produce
alternating electrical signals, as do all sorts of natural and man-made objects and
devices. These signals are what engineers and technicians are most often interested in
when studying electronics, but signals come in many very different forms. To understand
complex signals, there is often a need to simplify them; if the signal can be understood
in its simplest form, then that understanding can be applied to the complex signal.
The Sine Wave
Many signal waves, tend to be repetitive, or "periodic". They repeat a particular pattern
or wave shape over a regular time period. The most important of all the different wave
shapes is the sine wave, because any periodic wave can be shown to be made up of a
series of pure sine waves, perhaps of many different frequencies and amplitudes. The
sine wave is important to electronics engineers because of its purity, it consists of only
a single frequency, it alternates regularly above and below its mid value at a constant
rate. In a musical note this rate, the frequency, would be referred to as the pitch of the
note. All waves except sine waves contain many different frequencies. They have one
dominant frequency called "the fundamental", plus (often many) others called
"harmonics", that give a wave its particular character.
Rather than looking at how a circuit acts with complex periodic waves, that are made up
of a series of pure sine waves, it is much easier to use single sine waves. Measuring
sine waves is therefore important as the results obtained are a major source of
information in understanding the operation of electronic systems of many kinds.
Measuring the Sine Wave.
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What you´ll learn in Module 1.2
• Know measurements associated with sine waves
• a. Peak to peak value.
• b. Amplitude.
• c. Peak value.
• d. Periodic time.
• e. Average value.
• f. RMS value.
Fig 1.2.1 Characteristics of a Sine Wave
A wave form is a graph showing the variation, usually of voltage or current, against time.
The horizontal axis shows the passing of time, progressing from left to right. The vertical
axis shows the quantity measured (this is voltage in Fig 1.2.1).
Six of the most important characteristics of a sine wave are;
PEAK TO PEAK value.
INSTANTANEOUS value.
AMPLITUDE.
PEAK value.
PERIODIC TIME.
AVERAGE value.
RMS value.
These characteristics are illustrated in fig 1.2.1
Peak to Peak value
The PEAK TO PEAK value is the vertical distance between the top and bottom of the
wave. It will be measured in volts on a voltage waveform, and may be labelled V PP or
VPK−PK. In a current waveform it would be labelled IPP or IPK−PK as I (not C) is used to
represent current.
Instantaneous Value
This is the value (voltage or current) of a wave at any particular instant. often chosen to
coincide with some other event. E.g. The instantaneous value of a sine wave one quarter
of the way through the cycle will be equal to the peak value. See point X in Fig 1.2.1.
Amplitude
The AMPLITUDE of a sine wave is the maximum vertical distance reached, in either
direction from the centre line of the wave. As a sine wave is symmetrical about its centre
line, the amplitude of the wave is half the peak to peak value, as shown in Fig 1.2.2.
Fig 1.2.2 Defining the Peak value VPK
Peak value
The PEAK value of the wave is the highest value the wave reaches above a reference
value. The reference value normally used is zero. In a voltage waveform the peak value
may be labelled VPK or VMAX (IPK or IMAX in a current waveform).
If the sine wave being measured is symmetrical either side of zero volts (or zero
amperes), meaning that the dc level or dc component of the wave is zero volts, then the
peak value must be the same as the amplitude, that is half of the peak to peak value.
However this is not always the case, if a dc component other than zero volts is also
present, the sine wave will be symmetrical about this level rather than zero. The bottom
waveform in Fig 1.2.2 shows that the peak value can now be even larger than the peak
to peak value, (the amplitude of the wave however, remains the same, and is the
difference between the peak value and the "centre line" of the waveform).
Periodic Time & Frequency
The PERIODIC TIME (given the symbol T) is the time, in seconds milliseconds etc.
taken for one complete cycle of the wave. It can be used to find the FREQUENCY of
the wave ƒ using the formula T =1/ƒ
Thus if the periodic time of a wave is 20ms (or 1/50th of a second) then there must be
50 complete cycles of the wave in one second. A frequency of 50 Hz. Note that when
you use this formula, if the periodic time is in seconds then the frequency will be in Hz.
Fig 1.2.3 Determining the Average Value of a Sine Wave
The AVERAGE value. This is normally taken to mean the average value of only half a
cycle of the wave. If the average of the full cycle was taken it would of course be zero,
as in a sine wave symmetrical about zero, there are equal excursions above and below
the zero line.
Using only half a cycle, as illustrated in fig 1.2.3 the average value (voltage or current)
is always 0.637 of the peak value of the wave.
VAV = VPK x 0.637
or
IAV = IPK X 0.637
The average value is the value that usually determines the voltage or current indicated
on a test meter. There are however some meters that will read the RMS value, these
are called "True RMS meters".
The RMS Value.
The RMS or ROOT MEAN SQUARED value is the value of the equivalent direct (non
varying) voltage or current which would provide the same energy to a circuit as the sine
wave measured. That is, if an AC sine wave has a RMS value of 240 volts, it will provide
the same energy to a circuit as a DC supply of 240 volts.
It can be shown that the RMS value of a sine wave is 0.707 of the peak value.
VRMS = VPK x 0.707 and IRMS = IPK x 0.707
Also, the peak value of a sine wave is equal to 1.414 x the RMS value.
The Form Factor
If VAV (0.637) is multiplied by 1.11 the answer is 0.707, which is the RMS value. This
difference is called the Form Factor of the wave, and the relationship of 1.11 is only true
for a perfect sine wave. If the wave is some other shape, either the RMS or the average
value (or both) will change, and so will the relationship between them. This is important
when measuring AC voltages with a meter as it is the average value that most meters
actually measure. However they display the RMS value simply by multiplying the voltage
by 1.11. Therefore if the AC wave being measured is not a perfect sine wave the reading
will be slightly wrong. If you pay enough money however, you can buy a true RMS meter
that actually calculates the RMS value of non-sine waves.
The Mains (Line) Supply
To demonstrate some of these characteristics in use, consider a very common sine
wave, the mains supply or line waveform, which in many parts of the world is a nominal
230V.
Electrical equipment that connects to the mains supply always carries a label giving
information about what supply the equipment can be connected to. These labels are
quite variable in appearance, but often there is a picture of a sine wave showing that an
a.c. supply must be used. The voltage quoted will be 230V (or 120V in the USA)or range
of voltages including these values. These voltages actually refer to the RMS value of
the mains sine wave. The label also states that the frequency of the supply, which is
50Hz in Europe or 60Hz in the USA.
From this small amount of information other values can be worked out:
a. The peak voltage of the waveform, as VPK = VRMS x 1.414
b. The AVERAGE value of the waveform, as VAV = VPK x 0.637
c. The PEAK TO PEAK value of the waveform. This is twice the AMPLITUDE, which
(because the mains waveform is symmetrical about zero volts) is the same value as
VPK.
Because VPK is already known from a. it follows that VPP = VPK x 2
d.The PERIODIC TIME which is given by T =1/ƒ
AC Waves
1.
If a sine wave has a RMS voltage of 12volts, what will be its Peak-to-Peak
voltage?
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a) 33.9V
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b) 8.484V
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c) 16.9V
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d) 15.3V
2.
What is the peak value of a sine wave whose V AV value is 15V ?
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a) 19V
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b) 9.5V
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c) 21.2V
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d) 23.5V
3.
If an AC waveform has a periodic time of 2ms, what will be its frequency?
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a) 2kHz
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b) 500Hz
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c) 2MHz
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d) 50Hz
4.
With reference to Fig 1.3.1, what is the value labelled A?
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a) Periodic time
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b) Amplitude
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c) Frequency
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d) RMS value
5.
With reference to Fig 1.3.1, if the level labelled X has a value of 2V what is the
value labelled B?
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a) The Root Mean Squared value.
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b) The Amplitude.
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c) The Average value.
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d) The Peak value.
6.
In Fig 1.3.2, how many complete cycles are
shown?
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a) 2
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b) 3
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c) 4
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d) 7
7.
What value is given by the formula VPK x 0.637?
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a) VRMS
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b) VMAX
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c) The Form Factor
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d) VAV